but they will be repairing it with a defective part. If you spend $200 getting it fixed, your machine will be worth $400 at best so you'd probably be best selling it for parts and putting the money towards a better machine.

There's a possibility it's something other than the GPU but the display artifacts are symptoms of a bad GPU and it's a known issue with your model of computer.

Yeah definitely a GPU error, like said in the message above it doesn't make any sense to let the problem fixed. Although you can always try to contact Apple and see what they can do for you, best way to do this is to visit a local Apple Store. Good luck!